Difference between revisions of "E (mathematics)"
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(Correct use of the original article title should reflect the alphabetical letter) |
(the slope of the exponential curve is the same as its value) |
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'''''e''''' is a useful [[mathematical]] constant which is a [[transcendental]] number approximately equal to 2.718281828459045 . ''e'' can be used in [[logarithm]]s as the base, called a [[natural logarithm]]. ''e'' is named for [[Swiss]] [[mathematician]] [[Leonhard Euler]], though he did not discover the constant. | '''''e''''' is a useful [[mathematical]] constant which is a [[transcendental]] number approximately equal to 2.718281828459045 . ''e'' can be used in [[logarithm]]s as the base, called a [[natural logarithm]]. ''e'' is named for [[Swiss]] [[mathematician]] [[Leonhard Euler]], though he did not discover the constant. | ||
| − | It has some remarkable properties | + | It has some remarkable properties. For example, the slope of the exponential curve is the same as its value: |
:<math>\frac{d}{dx}e^x = e^x.</math> | :<math>\frac{d}{dx}e^x = e^x.</math> | ||
| − | (i.e. the | + | (i.e. the exponential function is an [[eigenfunction]] of the [[derivative]] operator, with [[eigenvalue]] 1). |
==Formulae for ''e''== | ==Formulae for ''e''== | ||
Revision as of 20:13, July 8, 2008
e is a useful mathematical constant which is a transcendental number approximately equal to 2.718281828459045 . e can be used in logarithms as the base, called a natural logarithm. e is named for Swiss mathematician Leonhard Euler, though he did not discover the constant.
It has some remarkable properties. For example, the slope of the exponential curve is the same as its value:
(i.e. the exponential function is an eigenfunction of the derivative operator, with eigenvalue 1).
Formulae for e
- With limits -
- With infinite series -
